Which of the following numbers is a factor of 105? ${5,6,10,12,13}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $105$ by each of our answer choices. $105 \div 5 = 21$ $105 \div 6 = 17\text{ R }3$ $105 \div 10 = 10\text{ R }5$ $105 \div 12 = 8\text{ R }9$ $105 \div 13 = 8\text{ R }1$ The only answer choice that divides into $105$ with no remainder is $5$ $ 21$ $5$ $105$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $105$ $105 = 3\times5\times7 5 = 5$ Therefore the only factor of $105$ out of our choices is $5$. We can say that $105$ is divisible by $5$.